We investigate the existence of multiple nontrivial solutions (${xi}$, ${eta}$) for perturbations $g_1$, $g_2$ of the harmonic system with Dirichlet boundary condition $${Delta}^2{xi}+c{Delta}{xi}=g_1(2{xi}+3{eta});in;{Omega}\{Delta}^2{eta}+c{Delta}{eta}=g_2(2{xi}+3{eta});in;{Omega}$$ where we assume that ${lambda}_1$ < $c$ < ${lambda}_2$, $g^{prime}_1({infty})$, $g^{prime}_2({infty})$ are finite. We prove that the system has at least three solutions under some condition on $g$.